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Journal of Economic Theory 144 (2009) 1468–1488

www.elsevier.com/locate/jet

On the relevance of exchange rate regimesfor stabilization policy

Bernardino Adao a, Isabel Correia a,b,c, Pedro Teles a,b,c,∗

a Banco de Portugal, Portugalb Universidade Catolica Portuguesa, Portugal

c CEPR, London, United Kingdom

Received 10 October 2007; final version received 23 February 2009; accepted 24 February 2009

Available online 26 March 2009

Abstract

This paper assesses the relevance of the exchange rate regime for stabilization policy. Using both fiscaland monetary policy, we conclude that the exchange rate regime is irrelevant. This is the case independentlyof the severity of price rigidities, independently of asymmetries across countries in shocks and transmissionmechanisms. The only relevant conditions are on the mobility of labor and financial assets. The results canbe summarized with the claim that every currency area is an optimal currency area. However, with labormobility or tradable state-contingent assets, additional policy instruments would be required to establish theirrelevance result.© 2009 Elsevier Inc. All rights reserved.

JEL classification: E31; E50; E63; F20; F31; F33; F41; F42

Keywords: Optimal currency areas; Monetary union; Fixed exchange rates; Fiscal and monetary policy; Stabilizationpolicy; Labor mobility; Nominal rigidities

1. Introduction

This paper revisits the issues in the optimal currency area literature initiated by Mundell [24].What are the costs of a fixed exchange rate regime, or a monetary union, when there is a role forstabilization policy? We address this question allowing for heterogeneity in the shocks and the

* Corresponding author.E-mail address: [email protected] (P. Teles).

0022-0531/$ – see front matter © 2009 Elsevier Inc. All rights reserved.doi:10.1016/j.jet.2009.02.005


B. Adao et al. / Journal of Economic Theory 144 (2009) 1468–1488 1469

response to them, restrictions on the mobility of factors and incompleteness of asset markets, asis standard in the optimal currency area literature.

When different shocks hit different countries or when there are differences across countries inthe effects of shocks, monetary policy, that has a stabilization role because of some form of nom-inal rigidity, may have to react differently in the different countries. Because of this heterogeneityit is common to infer that there are costs of a common monetary policy, either through a fixedexchange rate regime or a monetary union. In the literature, these costs are taken to be higher thestronger are the asymmetries, the more severe are the nominal rigidities, the more pronounced isthe incompleteness of international asset markets, the less mobile is labor, and, finally, the lessable is fiscal policy in effectively stabilizing the national economies (Corsetti [12]).1

We take the standard approach in the literature on optimal fiscal and monetary policy afterLucas and Stokey [23], followed by many others. There, fiscal and monetary policy are decidedjointly by a Ramsey government that must raise distortionary taxes to pay for exogenous gov-ernment expenditures, so that the Pareto first best solution is not achievable.2 In our second bestenvironment, we show that the loss of the country specific monetary tool is of no cost. This istrue irrespective of the asymmetry in shocks or response to these and the severity of the nominalrigidities. The elements that are crucial in assessing the costs of a single monetary policy are thethree last ones in the list by Corsetti above, but labor mobility, and the completeness of interna-tional financial markets, work in opposite ways to the conventional wisdom. Fiscal and monetarypolicy are able to eliminate the costs of a monetary union only if labor is not mobile across coun-tries and private state-contingent debt is not traded internationally. Unless further instruments areconsidered.

We consider a standard two country model. Each country specializes in the production of acomposite tradable good, which aggregates a continuum of goods produced using labor only. La-bor is not mobile across countries. Money is used for transactions according to a cash-in-advanceconstraint on the purchases of the two composite goods by the households of each country. Thegovernment of each country must finance exogenous expenditures on the good produced at homewith distortionary taxes and seigniorage. The tax instruments are labor income and consumptiontaxes. There is state-contingent private debt inside each country in zero net supply and noncon-tingent nominal public debt in each currency that can be traded internationally.

We start by analyzing a benchmark economy where prices are flexible (Sections 2 and 3).We show that any equilibrium allocation in the flexible price, flexible exchange rates, economycan be implemented with fiscal and monetary policies that induce stable producer prices andconstant exchange rates. This result has implications for economies under fixed exchange rateswith nominal rigidities (Section 4). For those policies, that under flexible prices keep pricesconstant, if firms were restricted in the setting of prices such as in Calvo [7], those restrictionswould be irrelevant and the same allocations could still be implemented. It follows that understicky prices and fixed exchange rates it is always possible to achieve the same allocations asunder flexible prices and exchange rates.

Under sticky prices there are equilibrium allocations other than the ones achieved under flexi-ble prices. We show that the common set of allocations to flexible and sticky prices dominates inwelfare terms those other equilibrium allocations. The reason for this result is the one in Diamondand Mirrlees [16], that even in a second best environment it is not optimal to distort production.

1 See also Corsetti [13].2 Lump-sum taxes are excluded for distribution reasons. If there were both distortionary and lump-sum taxes, the

irrelevance results would still be obtained. It would be possible, in that case, to attain the first best allocations.


1470 B. Adao et al. / Journal of Economic Theory 144 (2009) 1468–1488

With the two results, (i) that under fixed exchange rates and sticky prices it is possible to im-plement the set of allocations under flexible exchange rates and flexible prices and (ii) that theset of allocations under flexible prices is optimal, we are able to establish that the choice of theexchange rate regime is irrelevant for optimal stabilization policy.

When prices are sticky, one would think that flexible exchange rates would be useful inadjusting the relative price of goods to different shocks. In our model, because we allow forconsumption taxes, the relative price is the ratio of prices gross of consumption taxes, adjustedby the nominal exchange rate. When the exchange rate is fixed, consumption taxes have a directeffect on the relative price and move in response to shocks so that the necessary adjustments takeplace. Labor income taxes also have to be adjusted so that other margins are not affected.

Exchange rate policy can play other roles such as completing the noncontingent internationalfinancial markets.3 Again, when the exchange rates are fixed, taxes, and interest rates commonacross countries, play that same role of allowing for the returns on assets traded internationallyto vary with the shocks.

Labor immobility is an important assumption for our results (Section 5.1.1). Labor mobil-ity imposes additional equilibrium restrictions, in particular arbitrage conditions on the choiceof where to work, that cannot be satisfied with the policy instruments that we consider. Simi-larly, perfect capital mobility would also require further instruments, for the irrelevance resultsto hold (Section 5.1.2). These results go against the traditional claims in the optimal currencyarea literature.

Related literature reassesses Milton Friedman [20]’s case for exchange rate flexibility, as away of side-stepping the rigidity in relative price movements. Recent examples in the debate are,for instance, Devereux and Engle [15] and Duarte and Obstfeld [18]. Devereux and Engle [15]provide an example with local currency pricing where exchange rate flexibility is of no use. Be-cause the prices of goods are set in the currency of the consumers, the exchange rate cannotaffect the relative price. Duarte and Obstfeld [18] respond, showing that exchange rate flexibilitycan still be of use in a more complex environment with nontradable goods. Even if exchangerate movements cannot affect the relative price of goods, they can still affect the allocations andimprove welfare. Because the optimal exchange rate regime depends on the degree of exchangerate pass-through, Corsetti and Pesenti [14] endogenize the decision on which currency pricesare set in. They show that there are two self validating regimes, one with fixed and another withflexible exchange rates. The flexible exchange rate regime provides higher welfare. Our paperquestions the generality of the exercises in these papers. We show that the claims hinge on thefocus on monetary policy only.4 Once the choice of the exchange rate regime is considered in thecontext of the full choice of policy instruments including tax and debt policy, exchange rate flexi-bility can be replaced with a gain by fiscal instruments. In the set up of Devereux and Engle [15],the exchange rate regime would still be irrelevant, but it would be possible to implement betterallocations; the remark of Duarte and Obstfeld [18] would not go through; and the two regimesin Corsetti and Pesenti [14], flexible or fixed exchange rates, would provide the same welfare.

Cooper and Kempf [10] make a similar point to ours in a very different context. They explicitlymodel the Mundellian trade-off between the benefits of a monetary union in reducing transaction

3 See Chari, Christiano and Kehoe [8], Schmitt-Grohé and Uribe [27], Siu [28], Correia, Nicolini and Teles [11], andAiyagari, Marcet, Sargent and Seppala [1] for optimal policy without state contingent public debt in a closed economy.See also Angeletos [2], and Buera and Nicolini [6], on the use of debt of different maturities as a way of completing assetmarkets.

4 For recent work on optimal monetary policy in a currency area see Benigno [4].



costs and the costs of the union in the ability to stabilize. Stabilization in their set up are risksharing transfers between agents. If the government is able to stabilize using alternative fiscalinstruments, then there are no costs of a monetary union.

Gali and Monacelli [21] and Ferrero [19] consider both fiscal and monetary policy in a set upcloser to ours,5 but restrict the set of fiscal policy instruments. For that reason, they are unableto establish the irrelevance results that we obtain. In Gali and Monacelli [21] the governmentchooses the optimal level of public consumption in a monetary union with lump-sum taxes. Theuse of state-contingent public consumption is useful, but is not a substitute for exchange rateflexibility. Ferrero [19], like us, considers that lump-sum taxes are not available. He solves avery similar policy problem to ours with the main difference that consumption taxes are notconsidered. He allows for state-contingent labor income taxes, but not for consumption taxes. Asit turns out, that assumption is crucial. While we are able to establish that exchange rate flexibilityis irrelevant, in Ferrero [19] all fiscal policy does is help attain higher welfare. There is still a costof a monetary union.

We assume that both fiscal and monetary policy variables are state-contingent. Because ourquestion is a regime question, we think that the natural assumption is to allow for alternative fiscaland monetary institutions, other than the ones we observe. This was the approach in Lucas andStokey [23], followed by the subsequent literature (see Chari, Christiano and Kehoe’s multiplecontributions,6 Correia, Nicolini and Teles [11], Schmitt-Grohé and Uribe [27], Siu [28], Be-nigno and Woodford [5], and, in the open economy, Benigno and Paoli [3], Ferrero [19] amongothers). We do not think there are fundamental reasons for taxes not to be state-contingent. Ifthere were, then they should probably also apply to monetary policy, given that monetary policyacts essentially like fiscal policy, in the models that we use. But since we do observe that mon-etary policy is very flexible, most likely, there is nothing preventing fiscal policy from being asflexible.

The results and methodology in Correia et al. [11] are instrumental for the results we obtainhere. Correia et al. show, in the closed economy, that optimal allocations and policies do notdepend on whether prices are flexible or sticky. In this paper, we show that the results hold inthe open economy, as well, irrespective of the degree of price rigidity and of the form, whetherprices are set in the producer or the consumer currency. But, more important, we show thatsticky prices are irrelevant when exchange rates are fixed. This is not only counter intuitive, butit is also contrary to the existing results in the literature. It allows us to contribute to the literatureon optimal currency areas with a stark irrelevance result.

2. The model

The economy has two countries of equal size, the home country and the foreign country.In each country there is a representative household, a continuum of firms and a government.Each firm produces a distinct, perishable consumption good with labor only. In each periodt = 0,1, . . . , T , where T can be made arbitrarily large,7 the economy experiences one of finitely

5 There is related work on optimal fiscal and monetary policy in small open economies. In Nicolini and Hevia [25],even if prices are sticky, the second best, flexible price equilibrium is implementable, but exchange rates must moveacross states. See also Benigno and Paoli [3].

6 See, in particular, Chari, Christiano and Kehoe [8] and Chari and Kehoe [9].7 The assumption of a finite, even if arbitrarily large, time horizon considerable simplifies the analysis, and is as

reasonable an assumption as the more standard one of an infinite horizon.



many events st . The initial realization s0 is given. The set of all possible events in period t isdenoted by St , the history of these events up to and including period t , which we call state at t ,(s0, s1, . . . , st ), is denoted by st , and the set of all possible states in period t is denoted by St . Thenumber of all possible states in period t is #St . All the relevant variables for this world economyare a function of the state but to simplify the notation we do not index formally the variables tothe state.

There are markets for goods, labor, money, state-contingent debt and state-noncontingent debt.The labor market is segmented across countries. The state-contingent debt market is segmentedacross countries and across households and governments. The goods and the state-noncontingentdebt are tradable across countries and agents. In this section we assume that firms set prices everyperiod with contemporaneous information. We also assume that exchange rates are flexible.

2.1. The households

The preferences of the home households are described by the expected utility function

U = E0

T∑t=0

βtu(Ch,t ,Cf,t ,Lt ). (1)

Ch,t is the home composite consumption good that aggregates the goods produced by the homefirms,

Ch,t =[ 1∫

0

Ch,t (i)θ−1θ di

] θθ−1

, θ > 1, (2)

where Ch,t (i) is the consumption of the good produced by firm i. There is a continuum of homefirms indexed by i, in the unit interval. Cf,t is the foreign composite consumption good aggre-gating the goods produced by the foreign firms,

Cf,t =[ 1∫

0

Cf,t (j)θ−1θ dj

] θθ−1

. (3)

There is also a continuum of these firms, indexed by j , in the unit interval. Lt is leisure time andis equal to 1 − Nt, where Nt is total time devoted to production.

The preferences of the foreign households are described by

U = E0

T∑t=0

βtu(C∗

h,t ,C∗f,t ,L

∗t

),

where C∗h,t is the foreign households composite consumption of the goods produced in the

home country, according to C∗h,t = [∫ 1

0 C∗h,t (i)

θ−1θ di] θ

θ−1 , and C∗f,t is the foreign households

composite consumption of the goods produced in the foreign country, according to C∗f,t =

[∫ 10 C∗

f,t (j)θ−1θ dj ] θ

θ−1 .The households of either country minimize expenditure in the home and foreign goods to

obtain a given aggregate consumption of either good. This implies, for the home households,

Ch,t (i) =(

Ph,t (i)

Ph,t

)−θ

Ch,t and Cf,t (j) =(

P ∗f,t (j)

P ∗f,t

)−θ

Cf,t ,



with

Ph,t =[ 1∫

0

Ph,t (i)1−θ di

] 11−θ

and P ∗f,t =

[ 1∫0

P ∗f,t (j)1−θ dj

] 11−θ

,

where Ph,t (i) is the price of the good produced by the home firm i in units of domestic currency,and P ∗

f,t (j) is the price of the good produced by the foreign firm j in units of foreign currency.Expenditure in either composite good purchased by the home households can then be written as

1∫0

Ph,t (i)Ch,t (i) di = Ph,tCh,t and

1∫0

P ∗f,t (j)Cf,t (j) dj = P ∗

f,tCf,t .

Similar expressions are obtained for the households of the foreign country.The budget constraints can then be written in terms of the aggregate variables. The repre-

sentative household of the home country at the beginning of each period t = 0,1, . . . , T ,8 usesthe nominal wealth Wt to buy Mt (home money), Bh,t (home government noncontingent debt),Bf,t (foreign government noncontingent debt) and Bt+1 (home private state-contingent debt).The home government noncontingent debt pays the gross return Rt in the domestic currency atthe beginning of the following period, and the foreign government noncontingent debt pays grossreturn R∗

t in foreign currency. The price, normalized by the probability of occurrence of the state,at date t of one unit of domestic currency at a particular state at date t + 1 is Qt,t+1. There is nogovernment state-contingent debt and the home household cannot buy foreign contingent debt.The price of one unit of foreign currency in units of home currency is εt . Thus, the followingrestrictions must be satisfied, respectively, for the home and the foreign households,

Mt + Bh,t + εtBf,t + EtBt+1Qt,t+1 � Wt ,

M∗t + B∗

h,t

εt

+ B∗f,t + EtB

∗t+1Q

∗t,t+1 � W

∗t .

(4)

In the home country there are taxes on the consumption of home produced goods, τh,t , on theconsumption of foreign produced goods, τf,t , labor income τn,t and profits. As the tax on profitsis lump-sum, it is optimal that all profits be taxed away, so that the net profits are zero.9 Thereare corresponding taxes in the foreign country, τ ∗

h,t , τ ∗f,t , τ ∗

n,t .The wealth that home and foreign households bring to date t + 1 is, respectively,

Wt+1 = Mt − (1 + τh,t )Ph,tCh,t − (1 + τf,t )εtP∗f,tCf,t

+ Bh,tRt + εt+1Bf,tR∗t + Bt+1 + (1 − τn,t )WtNt ,

W∗t+1 = M∗

t − (1 + τ ∗

h,t

)Ph,t

εt

C∗h,t − (

1 + τ ∗f,t

)P ∗

f,tC∗f,t

+ B∗h,t

εt+1Rt + B∗

f,tR∗t + B∗

t+1 + (1 − τ ∗

n,t

)W ∗

t N∗t .

(5)

8 We assume that there is an additional subperiod at T + 1 with an assets market for the clearing of debts, whichguarantees that money has value in the finite horizon economy. Agents want to take money to period T + 1 to settledebts. If the finite horizon economy ended with a goods market at T , then sellers would not accept money in period T ,and therefore money would not have value, not only in that period but in every period.

9 This assumption that profits are fully taxed is without loss of generality.



Money is used to purchase goods according to the following cash-in-advance constraints, forthe home and foreign country, respectively,

(1 + τh,t )Ph,tCh,t + (1 + τf,t )εtP∗f,tCf,t � Mt, all st , 0 � t � T , (6)

(1 + τ ∗

h,t

)Ph,t

εt

C∗h,t + (

1 + τ ∗f,t

)P ∗

f,tC∗f,t � M∗

t , all st , 0 � t � T . (7)

The households of the home country take prices, policies and initial wealth as given andchoose allocations and asset positions that maximize expected utility (1) subject to the cash-in-advance constraints (6) and the budget constraints (4) and (5) for the home country, together withWT +1 � 0. The households of the foreign country solve a similar problem.

Among the first order conditions for the home and foreign households are the intertemporalconditions for the contingent assets,

Qt−1,t

uCh(t − 1)

Ph,t−1(1 + τh,t−1)= βuCh

(t)

Ph,t (1 + τh,t ), all st−1 and st |st−1, 1 � t � T , (8)

Q∗t−1,t

εt−1uC∗h(t − 1)

Ph,t−1(1 + τ ∗h,t−1)

= βεtuC∗h(t)

Ph,t (1 + τ ∗h,t )

, all st−1 and st |st−1, 1 � t � T , (9)

the intertemporal conditions for the noncontingent assets,

uCh(t − 1)

Ph,t−1(1 + τh,t−1)= βRt−1Et−1

[uCh

(t)

Ph,t (1 + τh,t )

], all st−1, 1 � t � T , (10)

εt−1uCh(t − 1)

Ph,t−1(1 + τh,t−1)= βR∗

t−1Et−1

[εtuCh

(t)

Ph,t (1 + τh,t )

], all st−1, 1 � t � T , (11)

uC∗h(t − 1)

Ph,t−1(1 + τ ∗h,t−1)

= βRt−1Et−1

[uC∗

h(t)

Ph,t (1 + τ ∗h,t )

], all st−1, 1 � t � T , (12)

εt−1uC∗h(t − 1)

Ph,t−1(1 + τ ∗h,t−1)

= βR∗t−1Et−1

[εtuC∗

h(t)

Ph,t (1 + τ ∗h,t )

], all st−1, 1 � t � T , (13)

and the intratemporal conditions,

uL(t)

uCh(t)

= Wt(1 − τn,t )

Ph,tRt (1 + τh,t ), all st , 0 � t � T , (14)

uCh(t)

uCf(t)

= (1 + τh,t )Ph,t

(1 + τf,t )εtP∗f,t

, all st , 0 � t � T , (15)

uL∗t(t)

uC∗f(t)

= W ∗t (1 − τ ∗

n,t )

P ∗f,tR

∗t (1 + τ ∗

f,t ), all st , 0 � t � T , (16)

uC∗h(t)

uC∗f(t)

= (1 + τ ∗h,t )Ph,t

(1 + τ ∗f,t )εtP

∗f,t

, all st , 0 � t � T . (17)

The budget constraints of the households of each country, (4) and (5), together with the ter-minal conditions WT +1 � 0 and W

∗T +1 � 0, can be written as intertemporal budget constraints,

that at the optimum hold with equality. For the home country those constraints are the following:



T∑s=t

EtQt,s+1[(1 + τh,s)Ph,sCh,s + (1 + τf,s)εsP

∗f,sCf,s − (1 − τn,s)WsNs

]

+T∑

s=t

EtQt,s+1

[Ms

(Qt,s

Qt,s+1− 1

)]= Wt , all st , 0 � t � T ,

where Qt,s = Qt,t+1 . . .Qs−1,s , 0 � t � T , t + 1 � s � T + 1, and Qt,t = 1. AlsoET QT,T +1 = 1

RT.

Using the marginal conditions, as well as the cash-in-advance constraints, in the intertemporalbudget constraints, we can rewrite the household budget constraints in the home country andforeign country, respectively, as

T∑s=t

βs−tEt

[(uCh

(s)Ch,s + uCf(s)Cf,s − uL(s)Ns

)]

= Wt

uCh(t)

Ph,t (1 + τh,t ), all st , 0 � t � T , (18)

T∑s=t

βs−tEt

[(uC∗

h(s)C∗

h,s + uC∗f(s)C∗

f,s − uL∗(s)N∗s

)]

= W∗t

uC∗f(t)

P ∗f,t (1 + τ ∗

f,t ), all st , 0 � t � T . (19)

2.2. The government

The government of each country includes both the fiscal authority and the monetary authority.We assume, as is standard in this literature, that aggregate public expenditures are exogenous.Each government only consumes goods produced by local firms, and chooses consumption ofeach good to minimize expenditure on the aggregate level of expenditures, Gt for the homecountry and G∗

t , for the foreign country, respectively,

Gt =[ 1∫

0

Gh,t (i)θ−1θ di

] θθ−1

,

G∗t =

[ 1∫0

G∗f,t (j)

θ−1θ dj

] θθ−1

,

where Gh,t (i) is the home government consumption of the good produced by firm i and G∗f,t (j)

is the foreign government consumption of the good produced in that country by firm j .The home government issues state-noncontingent debt, Bh,t +B∗

h,t , and money, Mst , and taxes

labor income and private consumption, as well as profits. The nominal financial liabilities of thehome government at the start of period t are W

gt , which can be financed by issuing money and

public debt

Mst + Bh,t + B∗

h,t = Wgt .

The nominal financial liabilities the home government brings to the next period are



Wg

t+1 = Mst + RtBh,t + RtB

∗h,t + Ph,tGt − τh,tPh,tCh,t − τf,t εtP

∗f,tCf,t

− τn,tWtNt − Πh,t ,

where Πh,t are the aggregate profits of the home firms that are fully taxed. We impose the termi-nal condition that government liabilities in the terminal period are zero,10

Wg

T +1 = 0. The homegovernment period t intertemporal budget constraint can then be written as

T∑s=t

EtQt,s+1[τh,sPh,sCh,s + τf,sεsP

∗f,sCf,s + τn,sWsNs + Πh,s − Ph,sGs

]

+T∑

s=t

EtQt,s+1Mss

(Qt,s

Qt,s+1− 1

)= W

gt , all st , 0 � t � T .

There is a similar condition for the government of the foreign country.

2.3. Firms

In each country there is a continuum of firms in the unit interval. Each firm produces a distinct,perishable consumption good with a technology that uses labor only. Each home firm i has theproduction technology

Yh,t (i) = AtNt (i), all st , 0 � t � T , (20)

where Yh,t (i) is the production of good i, Nt(i) is the labor used in the production of good i,and At is an aggregate technology shock in the home country. Good i can be used for private andpublic consumption, Yh,t (i) = Ch,t (i) + C∗

h,t (i) + Gt(i). The technology in the foreign countryis

Yf,t (j) = A∗t N

∗t (j ), all st , 0 � t � T , (21)

where the technology parameter A∗t is the same across firms but can be different from At . Each

good j produced in the foreign country can be consumed by households or by the foreign gov-ernment, Yf,t (j) = Cf,t (j) + C∗

f,t (j) + G∗t (j ).

Prices are flexible. The firms in the home country choose prices to maximize profits Πh,t (i) =Ph,t (i)Yh,t (i) − WtNt(i), given the demand functions

Yh,t (i) =(

Ph,t (i)

Ph,t

)−θ

Yh,t , all st , 0 � t � T ,

where Yh,t = Ch,t + C∗h,t + Gt , obtained using the demand functions of the home good at home

and abroad, and given the production functions (20).The home firms set a common price Ph,t (i) = Ph,t such that

Wt

Ph,t

= θ − 1

θAt , all st , 0 � t � T , (22)

and the foreign firms set P ∗f,t (j) = P ∗

f,t , such that

W ∗t

P ∗f,t

= θ − 1

θA∗

t , all st , 0 � t � T . (23)

10 This results from a no-Ponzi games condition imposed on both households and governments.



2.4. Equilibrium

We now define a flexible price equilibrium as allocations {Ch,t ,Cf,t ,Nt ,C∗h,t ,C

∗f,t ,N

∗t } asset

positions {Mt,Bh,t ,Bf,t ,Bt+1,M∗t ,B∗

h,t ,B∗f,t ,B

∗t+1}, prices and policies {Ph,t ,Wt ,Rt ,Qt,t+1,

τh,t , τf,t , τn,t ,MSt , εt } and {Pf,t ,W

∗t ,R∗

t ,Q∗t,t+1, τ

∗h,t , τ

∗f,t , τ

∗n,t ,M

∗St } for t = 0,1, . . . , T and

all st , such that,

(a) Given the initial wealth levels, prices and policy the households choose the relevant quanti-ties that solve their problems;

(b) Given prices and policy, the firms choose the relevant quantities that solve their problems;(c) For initial public liabilities the governments satisfy their budget constraints;(d) The markets are in equilibrium, implying that for all st , 0 � t � T ,

Ch,t + C∗h,t + Gt = AtNt , (24)

Cf,t + C∗f,t + G∗

t = A∗t N

∗t , (25)

MSt = Mt, (26)

M∗St = M∗

t , (27)

Bt+1 = 0, (28)

B∗t+1 = 0. (29)

The market clearing in the labor and noncontingent bond markets was already imposed.The equilibrium conditions that determine the allocations {Ch,t ,Cf,t ,Nt ,C

∗h,t ,C

∗f,t ,N

∗t },

asset positions {Mt,Bh,t ,Bf,t ,Bt+1,M∗t ,B∗

h,t ,B∗f,t ,B

∗t+1}, prices and policies {Ph,t ,Wt ,Rt ,

Qt,t+1, τh,t , τf,t , τn,t ,MSt , εt } and {Pf,t ,W

∗t ,R∗

t ,Q∗t,t+1, τ

∗h,t , τ

∗f,t , τ

∗n,t ,M

∗St } are (6)–(19),

(22)–(29) and the intertemporal budget constraints of the home country that can be obtained byadding up the home government budget constraints and the home household budget constraints,as follows,

T∑s=t

EtQt,s+1[Ph,s(Ch,s + Gs) + εsP

∗f,sCf,s − WsNs − Πh,s

]= W

et , all st , 0 � t � T , (30)

where Wet = Wt − W

gt are the net foreign assets owned by the home country. Using the market

clearing conditions and the expression for profits, those constraints can be written as

T∑s=t

EtQt,s+1[εsP

∗f,sCf,s − Ph,sC

∗h,s

] = Wet , all st , 0 � t � T . (31)

3. Equilibria under flexible prices

Our purpose in this section is to assert a major result of the paper that has implications forequilibrium allocations with sticky prices and fixed exchange rates. We show that the set ofequilibrium allocations under flexible prices and flexible exchange rates can be implementedwith policies such that the price level in either country is constant over time, and such that thenominal exchange rate is also constant over time. In order to do this we show that, for a given



equilibrium allocation {Ch,t ,Cf,t ,Nt ,C∗h,t ,C

∗f,t ,N

∗t }, the equilibrium conditions are all satisfied

with constant producer price levels in each country equal to arbitrary numbers, and a constantnominal exchange rate.

The proposition follows:

Proposition 1. Let Ph,0 and P ∗f,0 be arbitrary positive numbers. Any flexible equilibrium alloca-

tion can be implemented with Ph,t = Ph,0 and P ∗f,t = P ∗

f,0, and constant exchange rates, εt = ε0.

Proof. Without loss of generality we take T = 1. In the beginning of period t = 2 the assetsmarket opens to liquidate debts. This means that the wealth of the households in period t = 2, ineither country, is zero, W2 = 0 and W

∗2 = 0.

We take as given an arbitrary equilibrium allocation {Ch,t ,Cf,t ,Nt ,C∗h,t ,C

∗f,t ,N

∗t } for t =

0,1, in the set defined above. We show that there are constant prices with Ph,t = Ph,0, P ∗f,t =

P ∗f,0, and fixed exchange rates, εt = ε0, which implies that Rt = R∗

t , that satisfy the equilibriumequations for that allocation which are (6)–(19), (22)–(29) and (31).

First, this allocation satisfies trivially the two feasibility constraints, (24) and (25), as it isan equilibrium allocation. For given Ph,0, P ∗

f,0, we use the remaining equilibrium conditions todetermine the values for the policy variables and remaining prices.

The firms’ conditions

Wt

Ph,0= θ − 1

θAt , t = 0,1,

W ∗t

P ∗f,0

= θ − 1

θA∗

t , t = 0,1,

determine Wt and W ∗t . The period 0 intertemporal budget constraints for the two representative

households are

1∑t=0

βtE0[(

uCh(t)Ch,t + uCf

(t)Cf,t − uL(t)Nt

)] = W0uCh

(0)

Ph,0(1 + τh,0),

1∑t=0

βtE0[(

uC∗h(t)C∗

h,t + uC∗f(t)C∗

f,t − uL∗(t)N∗t

)] = W∗0

uC∗h(0)

Ph,0ε0

(1 + τ ∗h,0)

,

which are satisfied by appropriately choosing τh,0 and τ ∗h,0. Given a common process for the

nominal interest rate

Rt = R∗t

to be determined later, and τh,0 and τ ∗h,0, we can use

uCh(0)

(1 + τh,0)= βR0E0

uCh(1)

(1 + τh,1), (32)

uC∗h(0)

(1 + τ ∗h,0)

= βR0E0uC∗

h(1)

(1 + τ ∗h,1)

, (33)

uCh(1)Ch,1 + uCf

(1)Cf,1 − uL(1)N1 = W1uCh

(1)

Ph,0(1 + τh,1), s1 ∈ S1, (34)



uC∗h(1)C∗

h,1 + uC∗f(1)C∗

f,1 − uL∗(1)N∗1 = W

∗1

uC∗h(1)

Ph,0ε0

(1 + τ ∗h,1)

, s1 ∈ S1, (35)

to determine the levels of noncontingent assets, W1 and W∗1, and contingent taxes, τh,1, τ ∗

h,1.The marginal conditions for the state-contingent assets, (8) and (9), are satisfied by the choice

of Qt−1,t and Q∗t−1,t , t = 1. The intratemporal conditions

uL(t)

uCh(t)

= Wt(1 − τn,t )

Ph,0Rt(1 + τh,t ), t = 0,1,

uCh(t)

uCf(t)

= (1 + τh,t )Ph,0

(1 + τf,t )ε0P∗f,0

, t = 0,1,

uL∗t(t)

uC∗f(t)

= W ∗t (1 − τ ∗

n,t )

P ∗f,0Rt(1 + τ ∗

f,t ), t = 0,1,

uC∗h(t)

uC∗f(t)

= (1 + τ ∗h,t )Ph,0

(1 + τ ∗f,t )ε0P

∗f,0

, t = 0,1

are satisfied by the choice of tax rates, τn,t , τf,t , τ ∗n,t , τ ∗

f,t , for t = 0,1. The cash-in-advanceconstraints

(1 + τh,t )Ph,0Ch,t + (1 + τf,t )ε0P∗f,0Cf,t � Mt, t = 0,1,(

1 + τ ∗h,t

)Ph,0

ε0C∗

h,t + (1 + τ ∗

f,t

)P ∗

f,0C∗f,t � M∗

t , t = 0,1

are satisfied by the choice of Mt and M∗t , for t = 0,1.

The home country intertemporal budget constraints

We1 = 1

R1

[ε0P

∗f,0Cf,1 − Ph,0C

∗h,1

], s1 ∈ S1, (36)

We0 = 1

R0

[ε0P

∗f,0Cf,0 − Ph,0C

∗h,0

] + E0Q0,1

R1

[ε0P

∗f,0Cf,1 − Ph,0C

∗h,1

](37)

are satisfied by choices of the nominal interest rates in the two periods, R1 and R0, and the initialvalue of the nominal exchange rate, ε0. There are still degrees of freedom for the level of thenominal exchange rate, ε0, and the level of noncontingent total assets, W

e1.

The proof extends to any finite horizon economy, t = 0, . . . , T , with T arbitrarily large. �We have shown that for any equilibrium allocation, {Ch,t ,Cf,t ,Nt ,C

∗h,t ,C

∗f,t ,N

∗t }, the equi-

librium conditions can be satisfied by asset positions, prices and policies such that producerprices are constant and equal to arbitrary constants, Ph,t = Ph,0, P ∗

f,t = P ∗f,0, and exchange rates

are also constant, εt = ε0.Taxes play a particular role when equilibria have constant producer prices and exchange rates.

Since prices are constant and so is the exchange rate, consumption taxes in one good relative tothe other have to move if relative prices are to move, which is the case in general if there are dif-ferent shocks in different countries. Consumption taxes play another role, when nominal publicdebt is noncontingent, that of replicating state-contingent real debt. The price level gross of con-sumption taxes is the deflator of nominal debt, so that ex-post volatility of the consumption taxcan replicate state-contingent real debt, which is the role played by ex-post volatility of the pricelevel in Chari et al. [8]. We have assumed, as is standard in this literature, that internationally



traded assets are state-noncontingent. Nominal interest rates, that in a fixed exchange rate regimeare common across countries, can play the role of replicating state-contingent international debt.Consumption taxes also affect the households margin between consumption and labor. Laborincome taxes have to adjust to compensate those effects. Since prices are constant and technolo-gies in the two countries are varying, the nominal wages have to move in response to shocks, andmove differently in different countries.11 Money supply also has to move in response to shocks,in order to satisfy the cash-in-advance constraints.

One first implication of the result in the proposition is that fixed exchange rates do not restrictthe set of allocations under flexible prices. This is an interesting result in itself, in particular,since asset markets are incomplete in our model. However, the issue of whether there are costsof a fixed exchange rate regime is typically associated with the presence of some type of pricerigidity, as first argued by Friedman [20]. If prices are sticky and exchange rates are fixed, onewould think that there would be restrictions on the relative prices of the goods produced in thedifferent countries. That is not the case: The second implication of the proposition is that fixedexchange rates do not restrict the set of allocations when prices are sticky. In the following sectionwe assume that firms are restricted in the setting of prices.

4. Sticky prices

We assume that firms set prices as in Calvo [7] staggered price setting, which is a commonlyused assumption in the sticky price literature. We assume that the firms set prices in the domesticcurrency. In each country, starting from an historical common price,12 at every date, each firmcan optimally set its price with some probability, that can differ across countries. Because thereis a continuum of firms, the probability is also the share of firms that optimally revise the pricein each period.

In general, staggered price setting leads to inefficient differences in prices across firms. Al-though in a given country firms are otherwise identical, have the same linear technology and faceidentical demand functions, they may charge different prices. The only case in which this will notoccur is when firms that are able to change prices decide not to do it. The price setting restrictionsin this case will not be binding, and the producer price level in each country will be constant.The equilibrium conditions will be identical to the equilibrium conditions of the flexible priceeconomy when producer prices are constant over time.

Since, as stated in Proposition 1, under flexible prices it is possible to implement the full setof equilibrium allocations with constant prices and fixed exchange rates, it follows that, understicky prices, it is also possible to implement that same set, also with fixed exchange rates.

It is clear that under sticky prices there are allocations that are not implementable under flexi-ble prices. That is the case whenever otherwise identical firms set different prices. It turns out, aswe show in Appendix A, that the set of flexible price allocations dominates in terms of welfarethe set of allocations under sticky prices. Since agents are heterogeneous across countries, themeaning of welfare dominance is the usual one, of a potential Pareto movement where lump-sumtransfers between agents are implicitly assumed.

Independently of the exchange rate regime, for each allocation that can be implemented understicky prices there is one under flexible prices that can potentially improve welfare in both coun-

11 If wages were sticky, additional taxes would be needed to keep the wages received by the households constant, aswell.12 This would be the case in a steady state where the prices are constant over time and therefore the same across firms.



tries. The reason for this is that, in order for sticky prices to be relevant, because different firmsface different price setting restrictions, firms that use the same technology and face the same de-mand conditions would charge different prices. This means that production would be inefficientand the inefficiency in production is not optimal in this second best environment.13

This result relates to the one in Diamond and Mirrlees [16] that shows that it is not optimal totax intermediate goods when there are consumption taxes on the final goods.

The proposition follows.

Proposition 2. In a world economy with noncontingent bond markets and Calvo (1983) staggeredprice setting there is no cost of a fixed exchange rate regime, independently of the degree of pricerigidity.

Proof. In Proposition 1 we show that the set of allocations under flexible prices is implementedwith policies that generate constant prices, equal to arbitrary numbers, and constant exchangerates. For the policies that induce prices to be equal to the historical initial prices of the Calvofirms, Ph,0 and P ∗

f,0, the equilibrium conditions under Calvo [7] are exactly the same ones asunder flexible prices. This establishes that the flexible price set of allocations is implementableunder Calvo price setting, with fixed exchange rates. It remains to show that the set is optimal,in the sense that for every allocation in the set under sticky prices, there is one in the set underflexible prices that is a potential Pareto improvement. This is done in Appendix A. �

The result in this proposition can be extended to any other form of price stickiness, such asprices set in advance as in Ireland [22], Taylor [29] staggered prices, Rotemberg [26] adjustmentcosts of changing prices, or state-dependent pricing as in Dotsey, King and Wolman [17]. For thecase where prices are set in advance, let the initial prices Ph,0 and P ∗

f,0 be exogenously given andthe other period prices, Ph,t and P ∗

f,t , be set in advance for k periods, for a finite k. Proposition 1implies that adding those restrictions to the flexible price economy still allows to implement theset of allocations under flexible prices, in a fixed exchange rate regime. The argument of welfaredominance of the flexible price set also applies there.

We have assumed that prices are set in the currency of the producer. We could alternativelyhave assumed local currency pricing. The results would follow through. For the policies thatsupport constant producer prices and constant exchange rates, local currency pricing would nothave any impact. Contrary to what is argued extensively in the literature that does not allow forfiscal policy instruments, it does not make a difference whether prices are set in the currency ofthe producer or the consumer.

We have analyzed flexible versus fixed exchange rate regimes. The analysis clearly followsthrough in a monetary union.

5. Minimal set of instruments

In Appendix A, in order to show the optimality of flexible prices over sticky prices, we charac-terize the set of equilibrium allocations that can be implemented in the model of Sections 2 and 3.The model is without capital, without mobility of labor or state-contingent assets, with flexible

13 This result, that replicating flexible prices is optimal, would be straightforward in a first best, if sticky prices were thesole distortion. Instead, in a second best where there are other distortions, adding an additional distortion could improvewelfare.



prices and wages, and flexible exchange rates. The fiscal instruments are labor income taxes,taxes on the consumption of home and foreign goods in each country, and public debt is non-contingent. Because we are interested in the Pareto frontier, we assume that there are lump-sumtransfers across countries. The set of implementable allocations is characterized by two imple-mentability conditions,14 corresponding to the time zero budget constraints of the governments(or households) in each country – in the primal form, in terms of quantities – (42) and (43), andthe resource constraints for each of the two goods in each state, (44) and (45).

This implementable set looks like the one in Lucas and Stokey [23] for a closed economy,without capital, with flexible prices and wages. In the closed economy of Lucas and Stokey,with only one consumption good, the implementability conditions are the single implementabil-ity condition corresponding to the time 0 budget constraint of the single government, and theresource constraints for the single good, for each state. Lucas and Stokey [23] consider differentfiscal instruments. The taxes are labor income taxes only, and public debt is state-contingent.

What is the minimal set of instruments to implement the equilibrium allocations characterizedby those implementability and feasibility conditions in Appendix A, analogous to the ones inLucas and Stokey? How important are assumptions about the environment, flexible prices, fixedexchange rates versus flexible, labor mobility and mobility of assets, capital accumulation, forthat minimal set of instruments?

In the basic set up without mobility of labor or of state-contingent private assets, and withnoncontingent public debt, but with all prices flexible, including exchange rates and wages, theminimal set of instruments are labor income taxes, and one additional tax on one of the con-sumption goods in one of the countries, a total of three taxes for the two countries. The needfor this one additional tax is that in this model there are two agents and two goods. Without thatconsumption tax, the marginal rates of substitution between the two consumption goods wouldhave to be equal for the two agents, and that would be an additional implementability constraint.

Whether public debt is contingent or not is actually irrelevant for the implementable set sinceit is possible to replicate state-contingent debt with ex-post volatility of the price level, a pointmade in the closed economy by Chari et al. [8].

In this flexible price model, if the exchange rate was fixed, then the same set of equilibriumallocations could be implemented with one consumption tax in each country, so that there wouldbe then a total of four taxes, on labor income in each country and on one consumption good ineach country. This is a case where one instrument is replaced by another equivalent instrument.

The same implementable set, considered in Appendix A, can be achieved even if prices aresticky, in a fixed exchange rate regime, without state-contingent public debt, provided otherinstruments are used (Proposition 1). In order to neutralize the sticky price restrictions, theequilibria must be implemented with constant prices. Because of those additional constraintson prices, we need to use additional fiscal instruments. We assume that, in addition to laborincome taxes, there are consumption taxes on all goods, rather than in one good only.15

Consumption taxes on one good, possibly the domestic good, in each country have to play therole of price level volatility in replicating state-contingent public debt. They also play the role ofequating nominal interest rates to the real rates plus inflation gross of taxes. With fixed exchangerates, there is a need for consumption taxes in the two other consumption goods to implement

14 The lump-sum transfers are important so that there is not a third constraint, the intertemporal budget constraint of thecountry.15 If wages were sticky, in order to neutralize those restrictions, wages would have to be constant in equilibrium. Thiscould be achieved with additional tax instruments, such as payroll taxes.



the desired intratemporal margins across consumption goods. These are minimal instruments toattain the irrelevance results.

Adding further decisions by private agents, such as the choice of working in a different coun-try or holding assets in different currencies, or capital accumulation, requires further instruments.Without further instruments, a fixed exchange rate regime would not be costless. We now con-sider those three cases.

5.1. Labor mobility and completeness of financial markets

We have assumed that labor is not mobile across countries, and that financial markets are tosome extent segmented, since state-contingent debt can only be traded within the country. Wedo not think that labor mobility across countries at the business cycle frequency is in any wayrelevant. Still, the question of what would be the implications of labor mobility is of theoreticalinterest, specially because we obtain a very different result from the one in the literature. That isthe case, as well, for mobility of financial assets.

We show that absence of labor mobility is a necessary condition for the irrelevance results.We also show that if private state-contingent debt was traded internationally a similar resultwould be obtained. In either case, in order to obtain the irrelevance results, it would be necessaryto have further instruments. These could be differential taxes depending on where the incomeoriginates from, in the case of labor mobility, and state-contingent public debt for the case ofcapital mobility.

5.1.1. Labor mobilityWe assume, now, that workers can choose to work in foreign firms being taxed at home. They

consume at home. This is one way of modeling labor mobility. There are alternative ways, butthe same arguments go through.

For the home households, total labor Nt is split between work at home Nh,t and work abroadNf,t , Nt = Nh,t + Nf,t . Similarly, for the foreign country, N∗

t is split between N∗h,t , which is

labor abroad, and N∗f,t , labor at home, in the foreign country, N∗

t = N∗h,t + N∗

f,t . The marketclearing conditions in the goods market, (24) and (25), become

Ch,t + C∗h,t + Gt = At

[Nh,t + N∗

h,t

]and


t = A∗t

[Nf,t + N∗

f,t

].

The conditions of the households problems are the same except for an additional arbitrage con-dition on where to work, that equates the two wages,

Wt = εtW∗t . (38)

The price setting conditions for the firms are also unchanged. The home country budget con-straints (31) become

T∑s=t

EtQt,s+1[εsP

∗f,sCf,s − Ph,sC

∗h,s + WsN

∗h,s − εsW

∗s Nf,s

]= Wt − W

gt , all st , 0 � t � T .

Notice that full labor mobility implies one additional constraint per state to the equilibriumconditions, namely (38). The wage in the same currency must be equal across countries. This is



not possible to satisfy with fixed exchange rates. In particular, it is not possible to satisfy both thefirms price setting conditions (22) and (23), with Ph,t = Ph,0 and P ∗

f,t = P ∗f,0, and the arbitrage

condition (38) with εt = ε0.It follows that, if labor was mobile, the policy instruments considered above would not be

sufficient to implement the set of flexible equilibrium allocations with fixed exchange rates. Ad-ditional fiscal instruments would be needed. If it was possible to tax labor of migrants differently,then there would be again no costs of the exchange rate regime, with labor mobility.

In the Mundellian optimal currency area literature, labor mobility made the costs of a currencyarea lower. Labor mobility reduced the costs of Keynesian unemployment and, therefore, theneed for stabilization policy. We obtain the opposite result, for a very different reason. Labormobility makes it harder to establish the result that there are no costs of a monetary union, inthe sense that it would require more policy instruments. In our set up, more flexibility in privatedecisions makes the life of the planner harder.

The fact that with labor mobility there are costs of a fixed exchange rate regime, while thereare no such costs when labor is immobile, does not mean that labor mobility is undesirable. Weare not comparing environments with and without labor mobility, but rather environments withand without fixed exchange rates, when labor is immobile or when it is mobile.

5.1.2. Completeness of financial marketsWe have assumed that public debt was noncontingent and that state-contingent private debt

was traded only within the country. If public debt was state-contingent, the results would notbe affected. It would mean that there would be more instruments and, therefore, if we obtainedthe results with less instruments we would also obtain them with more. Since the private agentsalready had access to domestic state-contingent nominal assets, there would be no change inmarginal private decisions. The only difference in the equilibrium conditions would be that thebudget constraints (18) and (19) could then be satisfied with the choice of Wt and W

∗t because

these would be state-contingent.The interesting cases are the following two cases, (a) and (b): In both private state-contingent

debt is traded internationally. In (a) public debt is state-contingent, while, in (b), public debt isnot state-contingent.

In (b), the irrelevance results would not go through. The additional private decisions wouldadd equilibrium conditions that could not be satisfied with the existing instruments, with fixedprices and exchange rates. This result is analogous to the one on labor mobility. Instead in (a),the additional instruments provided by state-contingent public debt are enough to satisfy thoseadditional arbitrage conditions. We show this now.

Private state-contingent debt is traded internationally, and public debt is state-contingent. Ifprivate state-contingent debt can be traded internationally, then there are additional marginalconditions. The agents can arbitrage between the two nominal state-contingent assets, in the twocurrencies, so that the following conditions must be satisfied:

Qt−1,t = Q∗t−1,t εt−1

εt

, all st−1 and st |st−1, 1 � t � T .

With a constant exchange rate, these restrictions imply

uCh(t − 1)

βuCh(t)

1 + τh,t

1 + τh,t−1= uC∗

h(t − 1)

βuC∗h(t)

1 + τ ∗h,t−1

1 + τ ∗h,t

, all st−1 and st |st−1, 1 � t � T . (39)



It turns out that the supply of state-contingent public debt frees up enough instruments that canbe used to satisfy these conditions.

As mentioned above, because public debt is state-contingent, the budget constraints in pe-riod 1 in the two countries, (34) and (35), are now satisfied by the choice of W1 and W

∗1, so that

the consumption taxes, τh,1 and τ ∗h,1, are not restricted by these conditions. Because the state-

contingent assets are traded internationally, the home country budget constraints in period 1,(36), can be satisfied by the choice of W

e1, so that the nominal interest rates, R1, are free. The

country budget constraint for period t = 0, (37), determines ε0, so that R0 is also free.Given τh,0 and τ ∗

h,0, the intertemporal marginal conditions (32) and (33) are satisfied by thechoice of R0, and impose restrictions on τ ∗

h,1. The tax rates τh,1 are not restricted and, thereforecan be used to satisfy the arbitrage restrictions (39), above.

Private state-contingent debt is traded internationally and public debt is not state-contingent.If state-contingent private debt could be traded internationally, but public debt was not state-contingent, then it would not be possible to satisfy the arbitrage conditions (39). The consumptiontaxes would be used to replicate state-contingent public debt and to satisfy the intertemporal con-ditions (32) and (33), and there would not be enough degrees of freedom to satisfy the arbitrageconditions (39).

This result is analogous to the result on labor mobility. Also here, if financial markets wereintegrated, in the sense that private state-contingent assets could be traded internationally, thenthere would be costs of a fixed exchange rate regime. Unless, again, additional instruments wouldbe considered, such as state-contingent public debt, as shown in the case above.

5.2. Capital accumulation

With capital as an additional input, the production functions in the home and foreign countryare, Yh,t (i) = AtF (Kt−1(i),Nt (i)) and Yf,t (j) = A∗

t F (K∗t−1(i),N

∗t (j )), respectively. We as-

sume, for simplicity, that capital is produced at home, so that the market clearing conditions, inthe two countries, are Ch,t +C∗

h,t +Gt +Kt − (1 − δ)Kt−1 = AtF (Kt−1,Nt ), all st , 0 � t � T ,and Cf,t + C∗

f,t + G∗t + K∗

t − (1 − δ)K∗t−1 = A∗

t F (K∗t−1,N

∗t ), all st , 0 � t � T , where δ is the

depreciation rate.The flexible-price firm decisions, in each country, include the choice of the quantity of capital

given the rental price of capital, Ut and U∗t . Those decisions add the same number of equilibrium

conditions as unknowns.The households hold capital. Their arbitrage conditions are

RtPh,t = Et

[Ph,t+1 + (1 − τk,t+1)(Ut+1 − δPh,t+1)

], all st , 0 � t � T − 1, (40)

R∗t P ∗

f,t = Et

[P ∗

f,t+1 + (1 − τ ∗

k,t+1

)(U∗

t+1 − δP ∗f,t+1

)], all st , 0 � t � T − 1, (41)

where τk,t+1 and τ ∗k,t+1 are the capital income taxes in the two countries. In order to satisfy these

conditions when the interest rates are equal, Rt = R∗t , and the prices are constant, it is necessary

to use further instruments. The capital income taxes play that role.

6. Concluding remarks

In this paper we address the central issues in the literature on optimal currency areas usingthe approach of Ramsey optimal fiscal and monetary policy. In our set up, every currency area



is an optimal currency area, provided there are restrictions on the mobility of labor and financialassets. This extreme result is in sharp contrast with the literature on optimal currency areas, andcalls for the need to take into account fiscal policy when addressing those regime issues.

Under a flexible exchange rate regime, monetary policy in each country can freely respondto shocks; it may respond to country specific shocks or it may respond to common shocks indifferent ways. Instead, in a monetary union there is a unique monetary policy for the membersof the union. This implies restrictions in the use of policy; the exchange rate must be constant overtime and the nominal interest rate must be equal across countries. Are these restrictions relevantto achieve the optimal equilibrium allocations? Does the answer to this question change with theintroduction of nominal rigidities, like staggered price setting? Does it matter that internationalcapital markets are segmented, and that labor is not mobile?

The conventional, Mundellian, wisdom is that there are costs of a fixed exchange rate regime,or a monetary union, resulting from the loss in ability to use policy for stabilization purposes. Thecosts are taken to be higher the stronger are the asymmetries across countries in shocks and theirtransmission, and the stronger are the nominal rigidities. Instead, we show that in an environmentwith nominal rigidities, whatever the type of price setting, producer currency pricing or localcurrency pricing, the exchange rate regime, whether flexible or fixed exchange rates, is irrelevantonce fiscal policy instruments are taken into account. We also show that, in order for the costs ofthe monetary union to be zero, labor cannot be mobile, unless additional policy instruments wereused. Similarly, there must be restrictions on the mobility of financial assets.

One final comment: Friedman [20] made the point that, in a world with sticky prices, exchangerates should be flexible in order for relative prices to be adjusted. We make a further point that ina world where prices are sticky and exchange rates cannot move there are still policy instrumentsthat can replace the role of the price level and the exchange rate. Note that the adjustments infiscal policy are not automatic and would require a knowledge of the model and the shocks to befully effective. But the movements in exchange rates that would be necessary to accomplish thesame goal, could be market determined, but would not be automatic either. The information thatis necessary to conduct policy under flexible exchange rates so that the path for exchange ratesis a particular one is exactly the same information necessary to affect directly the relative pricesusing tax rates.

Acknowledgments

We thank the anonymous associate editor for very useful suggestions. We thank participants atthe 2007 SED Meetings in Prague, the Banco de Portugal/CEPR Conference on Exchange Ratesand Currencies, and at seminars at Cambridge University, IIES at Stockholm University, UCL,the European University Institute, ECB and Banca d’Italia. We gratefully acknowledge financialsupport of FCT.

Appendix A. Allocations under flexible and sticky prices

In this appendix we show that for each allocation under sticky prices, there is an allocationunder flexible prices that gives at least as high welfare to one country without reducing thewelfare of the other country.

Assuming that lump-sum transfers are feasible between countries, the set of implementableallocations under flexible prices {Ch,t ,Cf,t ,Nt ,C

∗h,t ,C

∗f,t ,N

∗t } as well as initial taxes, prices,

and exchange rate {τh,0, τ∗h,0,Ph,0, ε0} is characterized by the following conditions:



1∑t=0

βtE0[(

uCh(t)Ch,t + uCf

(t)Cf,t − uL(t)Nt

)] = W0uCh

(0)

Ph,0(1 + τh,0), (42)

1∑t=0

βtE0[(

uC∗h(t)C∗

h,t + uC∗f(t)C∗

f,t − uL∗(t)N∗t

)] = W∗0

uC∗h(0)

Ph,0ε0

(1 + τ ∗h,0)

, (43)

Ch,t + C∗h,t + Gt = AtNt , (44)


t = A∗t N

∗t . (45)

We do not impose as a restriction the budget constraint between countries, because we al-low for transfers between these. The remaining equilibrium conditions determine the policy andprices. Denote the set of allocations that satisfy these conditions by Ef .

Under sticky prices the set of equilibrium conditions cannot be summarized by a small setof implementability conditions as under flexible prices. The allocations {Ch,t ,Cf,t ,Nt ,C

∗h,t ,

C∗f,t ,N

∗t } are restricted by the same intertemporal budget constraints as in the flexible price

case above, (42) and (43). For given prices {Ph,t (i)

Ph,t,

Pf,t (j)

Pf,t}, they are restricted by the feasibility

conditions

(Ch,t + C∗

h,t + Gt

) 1∫0

(Ph,t (i)

Ph,t

)−θ

di = AtNt , (46)

(Cf,t + C∗

f,t + G∗t

) 1∫0

(Pf,t (j)

Pf,t

)−θ

dj = A∗t N

∗t , (47)

the conditions that define the aggregate price levels, Ph,t = [∫ 10 Ph,t (i)

1−θ di] 11−θ and P ∗

f,t =[∫ 1

0 P ∗f,t (j)1−θ dj ] 1

1−θ , as well as all the remaining equilibrium conditions. Let the set of alloca-tions that satisfy these restrictions be denoted by Es .

It is straightforward to show that D ≡ ∫ 10 (

Ph,t (i)

Ph,t)−θ di � 1 and D∗ = ∫ 1

0 (Pf,t (j)

Pf,t)−θ dj � 1 .

D = 1 when Ph,t (i)

Ph,t= 1, and D∗ = 1 when

Pf,t (j)

Pf,t= 1.

The set of allocations under flexible prices dominates the set under sticky prices, meaning thatfor each allocation in Es there is at least one allocation in Ef with at least one of the goods inlarger or equal quantity and none smaller. The intertemporal budget constraints are the same butthe feasibility conditions are different, being (46) and (47) more restrictive than (44) and (45),and there are additional equilibrium restrictions over Es that are absent from Ef . Moreover, therestrictions over the allocations under sticky prices are exactly the same only when Ph,t (i) = Ph,0and Pf,t (j) = Pf,0.

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